Question 1083363
We are given point (6, 9) and the line x = 5
:
the line x = 5 intersects the x axis at the point (5, 0) and is perpendicular to the x axis, here is the graph of x = 5
:
{{{ drawing( 300, 300, -10, 10, -15, 15,
  grid( 1 ),
  green (line( 5, 15, 5, -15 ))
) }}}
:
the definition of slope is (change in y) / (change in x)
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for our line x = 5, we see that every point on the line has an x value of 5 so our change in x is always 0 and division by 0 is indeterminate
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a line which is perpendicular to a given line has a slope equal to the negative reciprocal of the given line
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in our case that would be 0
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a line perpendicular to x = 5 is a line where the y coordinate is fixed
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in order for the line to go through the point (6, 9), we have y = 9
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again looking at our definition of slope the difference in y coordinates is 0(9-9) and x value differences are not = to zero, therefore the slope is 0
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here is a graph of y = 9 along with x = 5
:
{{{ drawing( 300, 300, -10, 10, -15, 15,
  grid( 1 ),
  green (line( 5, 15, 5, -15 )),
  red (line( 10, 9, -10, 9 ))
) }}}
: